THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n
Let be a commutative ring, and denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in are adjacent if and only if there exists where and such that , and . This def...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universitas Pattimura
2025-07-01
|
| Series: | Barekeng |
| Subjects: | |
| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15930 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849389556887977984 |
|---|---|
| author | Vika Yugi Kurniawan Bayu Purboutomo Nughthoh Arfawi Kurdhi |
| author_facet | Vika Yugi Kurniawan Bayu Purboutomo Nughthoh Arfawi Kurdhi |
| author_sort | Vika Yugi Kurniawan |
| collection | DOAJ |
| description | Let be a commutative ring, and denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in are adjacent if and only if there exists where and such that , and . This definition generalizes the notion of an idempotent divisor graph by involving a triple product, which allows deeper exploration of the combinatorial behavior of idempotents in rings. In this research, we investigate the properties of the triple idempotent graph of the ring of integers modulo n, denoted by . As a results, we establish that and , provided that the graph is connected. Furthermore, is Hamiltonian if n is a prime and , and Eulerian if n is a prime and . |
| format | Article |
| id | doaj-art-08cd9833567e49a3b60b9406a61aa061 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-08cd9833567e49a3b60b9406a61aa0612025-08-20T03:41:56ZengUniversitas PattimuraBarekeng1978-72272615-30172025-07-011932219222810.30598/barekengvol19iss3pp2219-222815930THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_nVika Yugi Kurniawan0Bayu Purboutomo1Nughthoh Arfawi Kurdhi2Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sebelas Maret, IndonesiaLet be a commutative ring, and denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in are adjacent if and only if there exists where and such that , and . This definition generalizes the notion of an idempotent divisor graph by involving a triple product, which allows deeper exploration of the combinatorial behavior of idempotents in rings. In this research, we investigate the properties of the triple idempotent graph of the ring of integers modulo n, denoted by . As a results, we establish that and , provided that the graph is connected. Furthermore, is Hamiltonian if n is a prime and , and Eulerian if n is a prime and .https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15930diametereuleriangirthhamiltonianring z_nthe triple idempotent graph |
| spellingShingle | Vika Yugi Kurniawan Bayu Purboutomo Nughthoh Arfawi Kurdhi THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n Barekeng diameter eulerian girth hamiltonian ring z_n the triple idempotent graph |
| title | THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n |
| title_full | THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n |
| title_fullStr | THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n |
| title_full_unstemmed | THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n |
| title_short | THE TRIPLE IDEMPOTENT GRAPH OF THE RING Z_n |
| title_sort | triple idempotent graph of the ring z n |
| topic | diameter eulerian girth hamiltonian ring z_n the triple idempotent graph |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15930 |
| work_keys_str_mv | AT vikayugikurniawan thetripleidempotentgraphoftheringzn AT bayupurboutomo thetripleidempotentgraphoftheringzn AT nughthoharfawikurdhi thetripleidempotentgraphoftheringzn AT vikayugikurniawan tripleidempotentgraphoftheringzn AT bayupurboutomo tripleidempotentgraphoftheringzn AT nughthoharfawikurdhi tripleidempotentgraphoftheringzn |